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1.10 G: Differentiation

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Question 231

(Solutions based entirely on graphical or numerical methods are not acceptable.)

The power consumption of a high-performance computing cluster, P P\,P in kilowatts, is modeled by the function

P(t)=0.8t2.5−128t+2000,t>0 P(t) = 0.8t^{2.5} - 128t + 2000, \quad t > 0 P(t)=0.8t2.5−128t+2000,t>0

where t t\,t is the time in hours since the start of a large-scale simulation.

a.

Solve the equation P′(t)=0P'(t) = 0P′(t)=0.

[3]
b.

Solve the equation P′′(t)=15P''(t) = 15P′′(t)=15.

[3]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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